Personal IT Experiences

Songs purchased on the iTunes Store can be copied to an unlimited number of computers. However, only five computers at a time can play your iTunes DRM-protected music*.

You can enable a computer to play your purchased music by authorizing it. You can remove a computer from the authorization list by deauthorizing it. Deauthorizing your computer does not erase your music files; it simply prevents your purchased music from playing until you authorize that computer again.

Apple - Support - iTunes Store - Authorization FAQ